Despite her lower ranking after a year of injury woes, Williams was a hot favourite to lift a fourth US Open title but ninth seeded Stosur ripped up the script with a brilliant 6-2 6-3 victory over her American opponent.
"It all hasn't sunk in yet but it's an incredible achievement for her to go through a grand slam," Stosur's father Tony told Australia's ABC Radio from his Gold Coast home on Monday.
"She's been wanting to do this for many, many years of course but to do it in America against an in-form Serena Williams is quite numbing really," he added after Stosur became the first Australian woman to win the US Open in 38 years.
"She was awesome, she owned it, there was no doubt about it, she was absolutely fantastic."
In a match played on the 10th anniversary of the September 11 attacks on New York, Williams let her frustration get the better of her in the second set and picked up a code violation for screaming at the umpire as her title hopes slipped away.
"I was concerned the complexion of the match would change because of the distraction, and it did to some degree," Tony Stosur added.
"The crowd was absolutely behind Serena and the pressure must have been enormous on Sam to keep it together, because those sort of things can turn the match around, but she kept it together to her credit.
Stosur said his 27-year-old daughter was still coming to terms with her win when she called her family after the match.
"We put her on speaker phone with everyone who was here watching the match," he said.
"I think she's a bit numb, she's obviously delighted but like we all are, it hasn't really sunk in yet."
Australia Prime Minister Julia Gillard believes the win will encourage more of her compatriots to take up tennis in a bid to emulate the success as she congratulated Stosur.
"She has shown great determination and skill to win the US Open and everyone involved with tennis in Australia will be celebrating with her today," Gillard said.
"This is a great achievement and shows the future of Australian tennis is on the rise."